Vomma (volga)
Vomma, also called volga or vega convexity, is the second-order option greek that measures how an option's vega changes when implied volatility changes. It is close to zero at the money and largest for out-of-the-money options, which is why wing options gain more than their vega suggests when volatility jumps.
Senzoukria · Glossary · Updated September 2026
At a glance
- Definition
- ∂Vega/∂σ = ∂²V/∂σ²
- Black-Scholes
- Vomma = Vega·d1·d2 / σ
- Where it is large
- Out-of-the-money wings; near zero at the money
Definition
Vomma is the second derivative of the option value with respect to implied volatility, or the rate at which vega changes as volatility moves. In Black-Scholes it equals vega × d1 × d2 / σ. At the money d1 and d2 are close to zero and of opposite sign, so vomma is almost nil; away from the strike, d1 and d2 share a sign and vomma turns positive. A long option position therefore has convexity in volatility: its value rises faster than linearly when implied volatility climbs.
Worked example
Take a 30-day put struck at 90 with spot 100, implied volatility 25% and zero rates. Its Black-Scholes value is 0.213, its vega 0.037 per volatility point and its vomma 0.0032 per point squared. If implied volatility jumps to 30%, a vega-only estimate gives 0.213 + 5 × 0.037 = 0.397. Adding the vomma term, ½ × 0.0032 × 5² = 0.040, gives 0.437, close to the exact repriced value of 0.434. For the at-the-money option of the same maturity, vomma is about −0.000006 per point squared and the vega estimate is already accurate.
Vomma and the shape of the smile
Because wing options have positive vomma, a holder benefits from large swings in implied volatility and a seller is exposed to them. Practitioner pricing methods for the smile, such as the vanna-volga approach used in currency options, add a charge for vanna and vomma to the flat-volatility price, which is one way of explaining why out-of-the-money options trade at higher implied volatilities than the at-the-money option. It is an explanation of structure, not a forecast of where implied volatility will go.
- Short wing options, as in an iron condor, carry negative vomma: a volatility spike hurts more than vega alone predicts.
- Vomma matters most for large volatility moves; for a one-point change the vega estimate is usually enough.
- The VVIX index prices the volatility of the VIX itself, which is the market's view of how much volatility may move.
In Senzoukria
Senzoukria does not compute or display vomma. Its GEX Surface page can plot gamma exposure, vanna exposure, charm exposure, open interest and implied volatility across strikes and expiries, and its Volatility page reads the implied volatility smile and term structure of the loaded chain. The smile's wings, where vomma lives, are visible there as the out-of-the-money implied volatilities drawn on each side of spot.
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Frequently asked questions
- Why is vomma near zero at the money?
- At the money, d1 and d2 are both close to zero, so their product is tiny. Vega is already at its maximum there and barely changes when volatility moves, which is exactly what a vomma near zero says.
- Is volga the same thing as vomma?
- Yes. Volga (volatility gamma) is the name more common in currency options, vomma in equity texts. Both denote the second derivative of the option price with respect to implied volatility.